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The ratio of two numbers is 5 ∶ 6. If 3 is subtracted from both the numbers, the ratio becomes 2 ∶ 3. Find the sum of the two numbers. 


1. 9
2. 10
3. 11
4. 12

1 Answer

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Correct Answer - Option 3 : 11

Given

Ratio of two numbers = 5 ∶ 6

3 is subtracted from both number; find ratio = 2 ∶ 3

Formula Used

a ∶ b = c ∶ d

Product of Extremes = Product of Means

Calculation

Given ratio = 5 ∶ 6

Let the numbers be 5x and 6x; Sum of the numbers = 5x + 6x = 11x

According to Question,

(5x - 3) ∶ (6x - 3) = 2 ∶ 3

⇒ 15x - 9 = 12x - 6

⇒ 15x - 12x = 9 - 6

⇒ 3x = 3

⇒ x = 1

Sum of numbers = 11x = 11 × 1 = 11

The required sum is 11.

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